Chord AB subtracts a 75-degree arc and chord AC subtends a 112-degree arc. Find the BAC angle.

There are two options for the location of points A, B, C on a circle.

In the first version, the chords AB and AC are located on opposite sides of the point A.

Then the degree measure of the arc BC will be equal to: BC = 360 – AB – AC = 360 – 75 – 112 = 173.

Then the angle BAC = BC / 2 = 173/2 = 86.5.

In the second case, chords AB and AC are located on the same side of point A.

Then the degree measure of the arc BC will be equal to: BC = AC – AB = 112 – 75 = 37.

Then the angle BAC = BC / 2 = 37/2 = 18.5.

Answer: The angle BAC is 86.5 or 18.5.